Subtyping and Variance
Although Rust doesn't have any notion of structural inheritance, it does include subtyping. In Rust, subtyping derives entirely from lifetimes. Since lifetimes are scopes, we can partially order them based on the contains (outlives) relationship. We can even express this as a generic bound.
Subtyping on lifetimes is in terms of that relationship: if 'a: 'b
("a contains
b" or "a outlives b"), then 'a
is a subtype of 'b
. This is a large source of
confusion, because it seems intuitively backwards to many: the bigger scope is a
subtype of the smaller scope.
This does in fact make sense, though. The intuitive reason for this is that if
you expect an &'a u8
(for some concrete 'a
that you have already chosen),
then it's totally fine for me to hand you an &'static u8
even if 'static != 'a
, in the same way that if you expect an Animal in Java, it's totally fine
for me to hand you a Cat. Cats are just Animals and more, just as 'static
is just 'a
and more.
(Note, the subtyping relationship and typed-ness of lifetimes is a fairly arbitrary construct that some disagree with. However it simplifies our analysis to treat lifetimes and types uniformly.)
Higher-ranked lifetimes are also subtypes of every concrete lifetime. This is because taking an arbitrary lifetime is strictly more general than taking a specific one.
Variance
Variance is where things get a bit complicated.
Variance is a property that type constructors have with respect to their
arguments. A type constructor in Rust is a generic type with unbound arguments.
For instance Vec
is a type constructor that takes a T
and returns a
Vec<T>
. &
and &mut
are type constructors that take two inputs: a
lifetime, and a type to point to.
A type constructor's variance is how the subtyping of its inputs affects the subtyping of its outputs. There are two kinds of variance in Rust:
- F is variant over
T
ifT
being a subtype ofU
impliesF<T>
is a subtype ofF<U>
(subtyping "passes through") - F is invariant over
T
otherwise (no subtyping relation can be derived)
(For those of you who are familiar with variance from other languages, what we
refer to as "just" variance is in fact covariance. Rust has contravariance
for functions. The future of contravariance is uncertain and it may be
scrapped. For now, fn(T)
is contravariant in T
, which is used in matching
methods in trait implementations to the trait definition. Traits don't have
inferred variance, so Fn(T)
is invariant in T
).
Some important variances:
&'a T
is variant over'a
andT
(as is*const T
by metaphor)&'a mut T
is variant over'a
but invariant overT
Fn(T) -> U
is invariant overT
, but variant overU
Box
,Vec
, and all other collections are variant over the types of their contentsUnsafeCell<T>
,Cell<T>
,RefCell<T>
,Mutex<T>
and all other interior mutability types are invariant over T (as is*mut T
by metaphor)
To understand why these variances are correct and desirable, we will consider several examples.
We have already covered why &'a T
should be variant over 'a
when
introducing subtyping: it's desirable to be able to pass longer-lived things
where shorter-lived things are needed.
Similar reasoning applies to why it should be variant over T. It is reasonable
to be able to pass &&'static str
where an &&'a str
is expected. The
additional level of indirection does not change the desire to be able to pass
longer lived things where shorted lived things are expected.
However this logic doesn't apply to &mut
. To see why &mut
should
be invariant over T, consider the following code:
fn overwrite<T: Copy>(input: &mut T, new: &mut T) {
*input = *new;
}
fn main() {
let mut forever_str: &'static str = "hello";
{
let string = String::from("world");
overwrite(&mut forever_str, &mut &*string);
}
// Oops, printing free'd memory
println!("{}", forever_str);
}
The signature of overwrite
is clearly valid: it takes mutable references to
two values of the same type, and overwrites one with the other. If &mut T
was
variant over T, then &mut &'static str
would be a subtype of &mut &'a str
,
since &'static str
is a subtype of &'a str
. Therefore the lifetime of
forever_str
would successfully be "shrunk" down to the shorter lifetime of
string
, and overwrite
would be called successfully. string
would
subsequently be dropped, and forever_str
would point to freed memory when we
print it! Therefore &mut
should be invariant.
This is the general theme of variance vs invariance: if variance would allow you to store a short-lived value into a longer-lived slot, then you must be invariant.
However it is sound for &'a mut T
to be variant over 'a
. The key difference
between 'a
and T is that 'a
is a property of the reference itself,
while T is something the reference is borrowing. If you change T's type, then
the source still remembers the original type. However if you change the
lifetime's type, no one but the reference knows this information, so it's fine.
Put another way: &'a mut T
owns 'a
, but only borrows T.
Box
and Vec
are interesting cases because they're variant, but you can
definitely store values in them! This is where Rust gets really clever: it's
fine for them to be variant because you can only store values
in them via a mutable reference! The mutable reference makes the whole type
invariant, and therefore prevents you from smuggling a short-lived type into
them.
Being variant allows Box
and Vec
to be weakened when shared
immutably. So you can pass a &Box<&'static str>
where a &Box<&'a str>
is
expected.
However what should happen when passing by-value is less obvious. It turns out that, yes, you can use subtyping when passing by-value. That is, this works:
# #![allow(unused_variables)] #fn main() { fn get_box<'a>(str: &'a str) -> Box<&'a str> { // string literals are `&'static str`s Box::new("hello") } #}
Weakening when you pass by-value is fine because there's no one else who
"remembers" the old lifetime in the Box. The reason a variant &mut
was
trouble was because there's always someone else who remembers the original
subtype: the actual owner.
The invariance of the cell types can be seen as follows: &
is like an &mut
for a cell, because you can still store values in them through an &
. Therefore
cells must be invariant to avoid lifetime smuggling.
Fn
is the most subtle case because it has mixed variance. To see why
Fn(T) -> U
should be invariant over T, consider the following function
signature:
// 'a is derived from some parent scope
fn foo(&'a str) -> usize;
This signature claims that it can handle any &str
that lives at least as
long as 'a
. Now if this signature was variant over &'a str
, that
would mean
fn foo(&'static str) -> usize;
could be provided in its place, as it would be a subtype. However this function
has a stronger requirement: it says that it can only handle &'static str
s,
and nothing else. Giving &'a str
s to it would be unsound, as it's free to
assume that what it's given lives forever. Therefore functions are not variant
over their arguments.
To see why Fn(T) -> U
should be variant over U, consider the following
function signature:
// 'a is derived from some parent scope
fn foo(usize) -> &'a str;
This signature claims that it will return something that outlives 'a
. It is
therefore completely reasonable to provide
fn foo(usize) -> &'static str;
in its place. Therefore functions are variant over their return type.
*const
has the exact same semantics as &
, so variance follows. *mut
on the
other hand can dereference to an &mut
whether shared or not, so it is marked
as invariant just like cells.
This is all well and good for the types the standard library provides, but
how is variance determined for type that you define? A struct, informally
speaking, inherits the variance of its fields. If a struct Foo
has a generic argument A
that is used in a field a
, then Foo's variance
over A
is exactly a
's variance. However this is complicated if A
is used
in multiple fields.
- If all uses of A are variant, then Foo is variant over A
- Otherwise, Foo is invariant over A
# #![allow(unused_variables)] #fn main() { use std::cell::Cell; struct Foo<'a, 'b, A: 'a, B: 'b, C, D, E, F, G, H> { a: &'a A, // variant over 'a and A b: &'b mut B, // variant over 'b and invariant over B c: *const C, // variant over C d: *mut D, // invariant over D e: Vec<E>, // variant over E f: Cell<F>, // invariant over F g: G, // variant over G h1: H, // would also be variant over H except... h2: Cell<H>, // invariant over H, because invariance wins } #}